切换拓扑企业创新时滞演化博弈
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摘要
针对切换拓扑企业创新时滞演化博弈演化趋势进行分析。首先,将企业节点化构建企业合作创新博弈网络,建立切换拓扑企业创新时滞演化博弈模型;其次,运用半张量积方法,将每个时刻企业博弈收益、策略局势演化和博弈网络的切换分别代数公式化,综合得到与切换拓扑企业创新时滞演化博弈过程等价的代数表达式,分析博弈演化特征;然后,设计控制输入,得到企业全部参与合作创新的充要条件;最后,通过仿真实例验证结论的可行性。
Aiming at the analysis of the evolution trend of enterprise innovation time-delay evolutionary game under switching topology,firstly,the cooperative game network is constructed by treating the enterprise as a node and using edges to represent the correlation between enterprises.Then,the model of the evolutionary game with time delays of enterprise cooperative innovation under switching topology is established.Secondly,the revenue of the game,the evolution of the strategic profile and the switching of game networks are formulated separately by semi-tensor product.The algebraic expression of the process of evolutionary game enterprise innovation under switching topology is obtained,and the characteristics of game evolution are analyzed.Thirdly,the control input is designed,the necessary and sufficient conditions for all enterprises to participate in cooperative innovation are obtained.Finally,example is provided to illustrate the theoretical result.
Aiming at the analysis of the evolution trend of enterprise innovation time-delay evolutionary game under switching topology,firstly,the cooperative game network is constructed by treating the enterprise as a node and using edges to represent the correlation between enterprises.Then,the model of the evolutionary game with time delays of enterprise cooperative innovation under switching topology is established.Secondly,the revenue of the game,the evolution of the strategic profile and the switching of game networks are formulated separately by semi-tensor product.The algebraic expression of the process of evolutionary game enterprise innovation under switching topology is obtained,and the characteristics of game evolution are analyzed.Thirdly,the control input is designed,the necessary and sufficient conditions for all enterprises to participate in cooperative innovation are obtained.Finally,example is provided to illustrate the theoretical result.
引文
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[19]Fu S H,Wang Y Z,Zhao G D.A matrix approach to the analysis and control of networked evolutionary games with bankruptcy mechanism[J].Asian Journal of Control,2017,19(2):1-11.
[20]Fu S H,Li H T,Zhao G D.Modeling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism[J].International Journal of Control,2017,91(5):1-27.
[21]赵爱武,杜建国,关洪军.需求偏好下企业环境创新行为路径与绩效[J].系统工程理论与实践,2016,36(4):958-965.Zhao Aiwu,Du Jianguo,Guan Hongjun.Trajectory of environment innovation behavior and performance in terms of preference evolution[J].Systems Engineering---Theory and Practice,2016,36(4):958-965.
[22]罗文.系统动力学仿真在互联网产业创新中的应用[J].计算机工程与应用,2014,50(17):254-258.Luo Wen.Application of system dynamics simulation in Internet industry innovation[J].Computer Engineering and Application,2014,50(11):254-258.
[23]Cheng D Z,Qi H S,Zhao Y.Analysis and control of boolean networks:A Semi-tensor product approach[J].Acta Automatica Sinica,2011,37(5):529-540.
[2]约瑟夫·熊彼特.经济发展理论[M],伊犁人民出版社,2004.
[3]原驰,于洪雷,杨德礼.基于强互惠理论的企业合作创新行为演化研究[J].运筹与管理,2017,26(11):169-175.Yuan Chi,Yu Honglei,Yang Deli.Research on the evolution of enterprise cooperative innovation behavior with reciprocity theory[J].Operations Research and Management Science,2017,26(11):169-175.
[4]单莹洁.供应链节点企业合作创新的“囚徒困境”分析[J].技术经济与管理研究,2009,(5):42-44.Shan Yingjie.Analysis of the prisoner's dilemma of enterprises cooperative innovation of supply chain node[J].Technoeconomics and Management Research,2009,(5):42-44.
[5]苏屹,陈凤妍.企业家地方政治关联对技术创新绩效影响研究[J].系统工程理论与实践,2017,37(2):365-378.Su Yi,Chen Fengyan.Effect of entrepreneur's political connections on technological innovation performance[J].Systems Engineering---Theory and Practice,2017,37(2):365-378.
[6]Cheng D Z,He F H,Qi H S,et al.Modeling,analysis and control of networked evolutionary games[J].IEEE Transactions on Automatic Control,2015,60(9):2402-2415.
[7]Cheng D Z,Xu T T,He F H,et al.Semi-tensor product approach to networked evolutionary games[J].Control Theory and Technology,2014,12(2):198-214.
[8]Guo P L,Wang Y Z,Li H T.Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method[J].Automatica,2013,49(11):3384-3389.
[9]Zhao G D,Wang Y Z.Formulation and optimization control of a class of networked evolutionary games with switched topologies[J].Nonlinear Analysis:Hybrid Systems,2016,22:98-107.
[10]Zhang K Z,Zhang L J.Controllability of probabilistic Boolean control networks with time-variant delays in states[J].Decision and Control,2013,(9):7211-7216.
[11]Zhang K Z,Zhang L J.Controllability and observability of Boolean control networks with time-variant delays in states[J].Science China Information Sciences,2016,24(9):1478-1484.
[12]Cheng D Z,Li C X,Zhang X,et al.Controllability of boolean networks via mixed controls[J].IEEE Control Systems Letters,2018,2(2):254-259.
[13]宋平平,李海涛,杨琪琪,等.多值逻辑网络的输出跟踪控制[J].控制理论与应用,2016,33(9):1200-1206.Song Pingping,Li Haitao,Yang Qiqi,et al.The pinning control for the output tracking of multi-valued logical networks[J].Control Theory and Applications,2016,33(9):1200-1206.
[14]Tian H,Zhang H G,Wang Z S,et al.Stabilization of k-valued logical networks by open-loop control via the reverse-transfer method[J].Automatica,2017,83:397-390.
[15]Li F F,Li H Y,Xie L H,et al.On stabilization and set stabilization of multivalued logical systems[J].Automatica,2017,80:41-47.
[16]武利琴,王金环,徐勇.一种基于半张量积的多层网络演化博弈方法[J].复杂系统与复杂性科学,2017,14(3):68-74.Wu Liqin,Wang Jinhuan,XU Yong.Multilayer evolutionary networked games based on semi-tensor product[J].Complex systems and complexity science,2017,14(3):68-74.
[17]Zhu B,Xia X H,Wu Z.Evolutionary game theoretic demand-side management and control for a class of networked smart grid[J].Automatica,2016,70:94-100.
[18]Zhu B,Xia K W,Xia X H.Game-theoretic demand-side management and closed-loop control for a class of networked smart grid[J].Control Theory and Applications,2017,11(13):2170-2176.
[19]Fu S H,Wang Y Z,Zhao G D.A matrix approach to the analysis and control of networked evolutionary games with bankruptcy mechanism[J].Asian Journal of Control,2017,19(2):1-11.
[20]Fu S H,Li H T,Zhao G D.Modeling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism[J].International Journal of Control,2017,91(5):1-27.
[21]赵爱武,杜建国,关洪军.需求偏好下企业环境创新行为路径与绩效[J].系统工程理论与实践,2016,36(4):958-965.Zhao Aiwu,Du Jianguo,Guan Hongjun.Trajectory of environment innovation behavior and performance in terms of preference evolution[J].Systems Engineering---Theory and Practice,2016,36(4):958-965.
[22]罗文.系统动力学仿真在互联网产业创新中的应用[J].计算机工程与应用,2014,50(17):254-258.Luo Wen.Application of system dynamics simulation in Internet industry innovation[J].Computer Engineering and Application,2014,50(11):254-258.
[23]Cheng D Z,Qi H S,Zhao Y.Analysis and control of boolean networks:A Semi-tensor product approach[J].Acta Automatica Sinica,2011,37(5):529-540.